Download ArticleDownload ArticleThis article was co-authored by Joseph Meyer. Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.
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You can calculate the volume of a cone easily once you know its height and radius and can plug those measurements into the formula for finding the volume of a cone. The formula for finding the volume of a cone is v = hπr2/3.[1]
Steps
Help Finding Volume of a Cone
Find the radius. If you already know the radius, then you can move on to the next step. If you know the diameter, divide it by 2 to get the radius.[2] If you know the circumference, divide it by 2π to get the diameter.[3] And if you don't know any of the measurements of the shape, just use a ruler to measure the widest pie circular base (the diameter) and divide that number by 2 to get the radius. Let's say the radius of this cone's circular base is .5 inches (1.3 cm).
Use the radius to find the area of the base circle. To find the area of the base circle, you can just use the same formula you'd use to find the area of a circle: A = πr2. Plug ".5" in for r to get A = π(.5)2 and square the radius and multiply it by the value of π to find the area of the circular base. π(.5)2 = .79 in.2.[4]Advertisement
Find the height of the cone. If you know it already, write it down. If you don't know it, use a ruler to measure it.[5] Let's say the height of the cone is 1.5 inches (1.3 cm). Make sure that the height of the cone is written in the same measurements as the radius.
Multiply the area of the base by the height of the cone. Multiply the area of the base, .79 in.2, by the height, 1.5 in. So, .79 in.2 x 1.5 in = 1.19 in.[6]3
Divide the product by three. Simply divide 1.19 in.3 by 3 to find the volume of a cone. 1.19 in.3/3 = .40 in.3. Always state the volume in cubic units because it's a measure of three-dimensional space.[7]EXPERT TIPJoseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.Math Teacher
Joseph Meyer
Math TeacherTo calculate the volume of a cone, use its height and radius. The formula is Volume = (1/3)πr²h. (1/3) is a fixed value, π is approximately 3.14, r² represents the square of the radius, and h is the height from tip to base center. This information can be useful in engineering and baking.
Community Q&A
- QuestionWhat if the given is slant height and base? How to find the volume of cone?
Community AnswerUse the Pythagorean Theorem to find the height, using the slant length as the hypotenuse and half the base as one side. - QuestionIf I double the height, will I double the volume?
DonaganTop AnswererYes. - QuestionHow do I find the volume of a cone if the diameter is given, not the radius?
Community AnswerSince the volume of a cone is pi times the radius squared times the height divided by 3, if you know the diameter, you simply divide by two to find the radius, which you then plug into the formula.
Video
Tips
- Make sure you have accurate measurements.Thanks
- Don't do this while there's still ice cream in the cone.Thanks
- Make sure the measurements are all in the same type/unit of measurement.Thanks
Expert Interview
Thanks for reading our article! If you’d like to learn more about math, check out our in-depth interview with Joseph Meyer.
References
- ↑ https://www.omnicalculator.com/math/cone-volume
- ↑ https://sciencing.com/radius-diameter-7254718.html
- ↑ https://sciencing.com/calculate-radius-circumference-7804860.html
- ↑ https://www.mathwarehouse.com/geometry/circle/area-of-circle.php
- ↑ https://www.cuemath.com/measurement/volume-of-cone/
- ↑ https://www.omnicalculator.com/math/cone-volume
- ↑ https://www.cuemath.com/measurement/volume-of-cone/
About This Article
To calculate the volume of a cone, start by finding the cone's radius, which is equal to half of its diameter. Next, plug the radius into the formula A = πr^2, where A is the area and r is the radius. Once you have the area, multiply it by the height of the cone. Finally, divide that number by 3 to find the volume of the cone. Remember to write your answer in cubic units. For helpful sheets you can print out and take with you, read on!
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